Improve conditional κ to 0.001717256973467 with credited routing-frame fusion

[DavidAriasC]

Change and mathematical scope

The complete twelve-source words in PR #2751 retain the rank-six frame that PR #2733 already refits on a different predecessor word. This contribution composes that credited rank-five refit with both complete twelve-source words and passes full finite native, supplier and modern outer admission.

The resulting conditional bound is κ ≈ 0.001717256973467002308270, an absolute gain of 0.000000115387118575970161 and a relative gain of 0.006719720697% over the pinned twelve-source predecessor. This is a small, fully priced improvement; the refit itself is credited work, not a new mechanism.

At B1151, register 515's frame path changes from 5→6→7 to 5→5→7: two rank-one recursive transports become one rank-two transport. Register 393's paid histogram is unchanged. Across 666 calls the complete delta is 666*(H2−2H1), which strictly lowers the moment for 0<a<1.

• Local profile: {1:2364,2:647,3:297,4:120,5:26,8:8}.
• Complete profile: {1:1591740,2:430902,3:204396,4:79920,5:22532,8:5328,32:1,48:26558}.
• Rank mass 4,816,512; live/physical stock 66,304/66,801; all 276,390 owner roles, 415 helpers and 72 private buffers remain charged. Scalar chronology, source recovery, arbitrary-input endpoint and cleanup remain unchanged.
• Exact root bracket: [0.001717256973467002308270, 0.001717256973467002308271]; κ is the lower endpoint minus 10^-46 + 10^-70.
• Fixed-word generic packing cap: <0.001750493235223; achieved complex endpoint is 98.10132018% of this relaxation cap.

The package retains the pending modern outer and all-size compiler, source-access, hosting/routing, precision/fixed-tape, recovery, BIT and analytic-transfer assumptions. It does not discharge the BIT H2 machine obligation or prove an unconditional multiplication theorem. The selected frontier remains unchanged; the larger difference from selected κ includes predecessor work and a different outer contract.

Task and overlap

Started from canonical main 6b6b3ab304ca60eab7493e73f264fd23c146be4c, priority revision 5, on research/routing-leaf-cost. Refreshed main 936fac15b1b1b59dc5285c713a77f9f3c07b2906 leaves the guidance and selected inputs unchanged. Only research/complex-routing-leaf-fusion/ is added.

Task card: scalar-to-moment; scope changed from the explicit routing/leaf request to this binding paid-complex transport. The unchanged complex supplier prevents a faster implementation of the already assumed BIT route/leaf contract alone from improving selected κ. PR #2399 already covers conditional fast-callee substitution; PR #2457 covers spectator padding. This single bounded pivot supplies an actual paid-profile gain.

Exact dependencies:

• PR #2751: 4cfbb0cc8314d7fb4e8e754545a49a42eb590a69.
• PR #2733: a63c55ff56aaa8645d64d1162d1f017b59ded42a.

Final overlap refresh covered 711 open PRs and 1,400 Discussion/comment/reply records, with complete pagination and no warnings. Both dependency heads remained unchanged. OVERLAP.json records the boundaries, including the separate native replay acceleration and BIT caller/storage work. Metadata search is not a novelty certificate.

Validation

python3.12 -B scripts/research_package.py --package research/complex-routing-leaf-fusion

All five registered commands passed in 13.94 seconds on Python 3.12.15 with an unchanged file inventory. They cover complete words, literal forward/dual maps, frames, cleanup, owner allocation, exact moments, packing cap, optimized independent implementations, Git-free replay and rejection controls. Separate source-binding review caught and fixed a stale-bytecode issue in the cap checker; the forged-cache control passes.

Four complete native five-stage chains and retained parent admission were freshly executed. The public full replay then explicitly reused their fully hash-authenticated same-session cache and passed complete supplier/strict outer admission in 196.77 seconds, preserving inherited controls plus the omitted-refit rejection. Exact commands, environments, patches, source manifests, receipts and execution coverage are in VALIDATION.md and evidence/.

python3 -m pip install -r research/complex-routing-leaf-fusion/requirements.txt
python3 -B research/complex-routing-leaf-fusion/full_replay.py --work /tmp/FRESH-routing-leaf

The one-shot default network-download path was not separately run end to end; the actual invocation used authenticated local source exports and the fresh same-session native cache. No hosted-CI, independent human review or formal verification claim.

Credit

Marius-Paul Dumitrean supplied the frame refit; Tekalign supplied joint twelve-source recovery. Mason Hale's assignments, Philippe Van Velzen's pre-life hosting, Jeremy Kothe's allocation, Douglas Colkitt's exact ceiling engine, and the retained native/BIT/outer lineage remain credited. Original source files and notices are retained unchanged. New work is Apache-2.0, prepared for David Arias with substantial OpenAI Codex assistance and separate mathematical and implementation agents.

Open next questions

The README and TASK.json record two concrete follow-ups: change a source/restoration boundary and price every resulting transport/cleanup/owner cost; or implement one named physical route/leaf boundary with a uniform fixed-tape cost proof. The first targets a larger paid-profile gain; the second targets an inherited theorem obligation. Neither is discharged by this finite composition.